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Lecture Notes On Projective And Injective Banach Spaces
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Book Synopsis Separably Injective Banach Spaces by : Antonio Avilés
Download or read book Separably Injective Banach Spaces written by Antonio Avilés and published by Springer. This book was released on 2016-03-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.
Book Synopsis Linear and Complex Analysis Problem Book 3 by : Victor P. Havin
Download or read book Linear and Complex Analysis Problem Book 3 written by Victor P. Havin and published by Springer. This book was released on 2006-12-08 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!
Book Synopsis Lecture Notes in Pure and Applied Mathematics by :
Download or read book Lecture Notes in Pure and Applied Mathematics written by and published by . This book was released on 1992 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Trends in Banach Spaces and Operator Theory by : Anna Kamińska
Download or read book Trends in Banach Spaces and Operator Theory written by Anna Kamińska and published by American Mathematical Soc.. This book was released on 2003 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.
Book Synopsis Linear and Complex Analysis Problem Book 3 by : Nikolaĭ Kapitonovich Nikolʹskiĭ
Download or read book Linear and Complex Analysis Problem Book 3 written by Nikolaĭ Kapitonovich Nikolʹskiĭ and published by Springer. This book was released on 1994 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references.
Book Synopsis Introduction to Banach Spaces: Analysis and Probability: Volume 2 by : Daniel Li
Download or read book Introduction to Banach Spaces: Analysis and Probability: Volume 2 written by Daniel Li and published by Cambridge University Press. This book was released on 2017-11-02 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.
Book Synopsis Analysis in Banach Spaces by : Tuomas Hytönen
Download or read book Analysis in Banach Spaces written by Tuomas Hytönen and published by Springer. This book was released on 2016-11-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.
Book Synopsis Mathematical Foundation of Programming Semantics by : Austin Melton
Download or read book Mathematical Foundation of Programming Semantics written by Austin Melton and published by Springer Science & Business Media. This book was released on 1986-10 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Röntgenbefund und die sich in ihm widerspiegelnde pathologische Anatomie sind neben dem klinischen Bild die wichtigsten Säulen, auf denen die Diagnostik von Knochengeschwülsten und geschwulstähnlichen Läsionen beruht. Radiologen und Pathologen stellen in diesem Buch Klinik, Radiologie und Histolgie der verschiedenen Knochenläsionen am Gliedmaßen- und Achsenskelett umfassend und synoptisch dar. Das umfangreiche Material resultiert aus einer fünfzehnjährigen interdisziplinären Zusammenarbeit. In einem einleitenden Kapitel werden die verschiedenen radiologischen (konventionelles Röntgenbild, CT, Kernspintomographie, Angiographie, transkutane Biopsie) und histologischen Untersuchungstechniken und ihre Wertigkeit beschrieben. Der radiologischen Befundungsmethodik von Knochengeschwülsten u.a. mit Hilfe der Lodwick-Graduierung und einem neueren Staging-System für Knochengeschwülste werden eigene Kapitel gewidmet. Im speziellen Teil des Buches erfolgt die Darstellung der einzelnen benignen und malignen Knochengeschwülste in einer systematischen Untergliederung in ihre Häufigkeit, Lokalisation, Alters- und Geschlechtsprädilektion, Klinik und Prognose, Histologie, Radiologie und Differentialdiagnose. Besonders die unter den Knochengeschwülsten und tumorähnlichen Läsionen häufig vorkommenenden Entitäten sind mit einem umfassenden Bildmaterial ausgestattet, um dem breiten Spektrum ihrer Morphologie gerecht zu werden. Durch das Verständnis klinischer, radiologischer und pathologisch-anatomischer Befunde werden Diagnostik und Therapie der Skelettläsionen sehr erleichtert. Die synoptische Art der Darstellung macht dieses Buch für alle Disziplinen, die sich mit Knochentumoren befassen, zu einem idealen Nachschlagewerk.
Book Synopsis Handbook of the Geometry of Banach Spaces by :
Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces
Book Synopsis Introduction to Banach Spaces: Analysis and Probability by : Daniel Li
Download or read book Introduction to Banach Spaces: Analysis and Probability written by Daniel Li and published by Cambridge University Press. This book was released on 2018 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.
Book Synopsis Lectures and Exercises on Functional Analysis by : Александр Яковлевич Хелемский
Download or read book Lectures and Exercises on Functional Analysis written by Александр Яковлевич Хелемский and published by American Mathematical Soc.. This book was released on with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
Book Synopsis Lectures on Amenability by : Volker Runde
Download or read book Lectures on Amenability written by Volker Runde and published by Springer. This book was released on 2004-10-12 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.
Author :Jesus M.F. Castillo Publisher :Springer Science & Business Media ISBN 13 :9783540633440 Total Pages :284 pages Book Rating :4.6/5 (334 download)
Book Synopsis Three-space Problems in Banach Space Theory by : Jesus M.F. Castillo
Download or read book Three-space Problems in Banach Space Theory written by Jesus M.F. Castillo and published by Springer Science & Business Media. This book was released on 1997-11-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.
Book Synopsis The Functional Analysis of Quantum Information Theory by : Ved Prakash Gupta
Download or read book The Functional Analysis of Quantum Information Theory written by Ved Prakash Gupta and published by Springer. This book was released on 2015-05-28 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting.
Book Synopsis Introduction to Operator Space Theory by : Gilles Pisier
Download or read book Introduction to Operator Space Theory written by Gilles Pisier and published by Cambridge University Press. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
Book Synopsis M-Ideals in Banach Spaces and Banach Algebras by : Peter Harmand
Download or read book M-Ideals in Banach Spaces and Banach Algebras written by Peter Harmand and published by Springer. This book was released on 1993-07-29 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.
Book Synopsis Complex Interpolation between Hilbert, Banach and Operator Spaces by : Gilles Pisier
Download or read book Complex Interpolation between Hilbert, Banach and Operator Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 2010-10-07 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces $X$ satisfying the following property: there is a function $\varepsilon\to \Delta_X(\varepsilon)$ tending to zero with $\varepsilon>0$ such that every operator $T\colon \ L_2\to L_2$ with $\T\\le \varepsilon$ that is simultaneously contractive (i.e., of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\varepsilon)$ on $L_2(X)$. The author shows that $\Delta_X(\varepsilon) \in O(\varepsilon^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $\theta>0$ (see Corollary 6.7), where $\theta$-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).
